The comparisons of uncertainty calculi from the last two Uncertainty Workshops have all used theoretical probabilistic accuracy as the sole metric. While mathematical correctness is important, there are other factors which should be considered when developing reasoning systems. These other factors include, among other things, the error in uncertainty measures obtainable for the problem and the effect of this error on the performance of the resulting system. There are some domains in which many of the interesting conditional probabilities can be objectively estimated. For example, census data allows various characterizations of individuals with a reasonable degree of confidence.

In an earlier paper, a new theory of measurefree "conditional" objects was presented. In this paper, emphasis is placed upon the motivation of the theory. The central part of this motivation is established through an example involving a knowledge-based system. In order to evaluate combination of evidence for this system, using observed data, auxiliary at tribute and diagnosis variables, and inference rules connecting them, one must first choose an appropriate algebraic logic description pair (ALDP): a formal language or syntax followed by a compatible logic or semantic evaluation (or model). Three common choices- for this highly non-unique choice - are briefly discussed, the logics being Classical Logic, Fuzzy Logic, and Probability Logic. In all three,the key operator representing implication for the inference rules is interpreted as the often-used disjunction of a negation (b => a) = (b'v a), for any events a,b. However, another reasonable interpretation of the implication operator is through the familiar form of probabilistic conditioning. But, it can be shown - quite surprisingly - that the ALDP corresponding to Probability Logic cannot be used as a rigorous basis for this interpretation! To fill this gap, a new ALDP is constructed consisting of "conditional objects", extending ordinary Probability Logic, and compatible with the desired conditional probability interpretation of inference rules. It is shown also that this choice of ALDP leads to feasible computations for the combination of evidence evaluation in the example. In addition, a number of basic properties of conditional objects and the resulting Conditional Probability Logic are given, including a characterization property and a developed calculus of relations.

This paper describes a heuristic Bayesian method for computing probability distributions from experimental data, based upon the normal distribution form of the influence diagram. An example illustrates its use in medical technology assessment. This approach facilitates the integration of results from different studies, and permits a medical expert to make proper assessments without considerable statistical training. There has been extensive research on the construction and manipulation of expert systems using probabilities as a measure for uncertainty. These systems are capable of recognizing considerable dependence and of learning from unreliable observations.

Poly-trees are singly connected causal networks in which variables may arise from multiple causes. This paper develops a method of recovering ply-trees from empirically measured probability distributions of pairs of variables. The method guarantees that, if the measured distributions are generated by a causal process structured as a ply-tree then the topological structure of such tree can be recovered precisely and, in addition, the causal directionality of the branches can be determined up to the maximum extent possible. The method also pinpoints the minimum (if any) external semantics required to determine the causal relationships among the variables considered.

Decision tree induction systems are being used for knowledge acquisition in noisy domains. This paper develops a subjective Bayesian interpretation of the task tackled by these systems and the heuristic methods they use. It is argued that decision tree systems implicitly incorporate a prior belief that the simpler (in terms of decision tree complexity) of two hypotheses be preferred, all else being equal, and that they perform a greedy search of the space of decision rules to find one in which there is strong posterior belief. A number of improvements to these systems are then suggested.

This paper demonstrates a methodology for examining the accuracy of uncertain inference systems (UIS), after their parameters have been optimized, and does so for several common UIS's. This methodology may be used to test the accuracy when either the prior assumptions or updating formulae are not exactly satisfied. Surprisingly, these UIS's were revealed to be no more accurate on the average than a simple linear regression. Moreover, even on prior distributions which were deliberately biased so as give very good accuracy, they were less accurate than the simple probabilistic model which assumes marginal independence between inputs. This demonstrates that the importance of updating formulae can outweigh that of prior assumptions. Thus, when UIS's are judged by their final accuracy after optimization, we get completely different results than when they are judged by whether or not their prior assumptions are perfectly satisfied.

Bayes belief networks and influence diagrams are tools for constructing coherent probabilistic representations of uncertain knowledge. The process of constructing such a network to represent an expert's knowledge is used to illustrate a variety of techniques which can facilitate the process of structuring and quantifying uncertain relationships. These include some generalizations of the "noisy OR gate" concept. Sensitivity analysis of generic elements of Bayes' networks provides insight into when rough probability assessments are sufficient and when greater precision may be important.

David Beckerman and Holly Jimison Medical Computer Science Group Knowledge Systems Laboratory Stanford University Medical School Office Building, Room 215 Stanford, California 94305 We examine a Bayesian approach for accommodating beliefs and preferences that are held with partial confidence. An important notion highlighted by the method is that additional modeling can be valuable when complete confidence is lacking. We develop a meta-decision-analytic approach to balance the benefits of additional modeling with associated costs. We show how the approach can be used during knowledge acquisition to focus the attention of a knowledge engineer or expert on parts of a decision model that deserve additional refinement.

This paper examines Bayesian belief network inference using simulation as a method for computing the posterior probabilities of network variables. Specifically, it examines the use of a method described by Henrion, called logic sampling, and a method described by Pearl, called stochastic simulation. We first review the conditions under which logic sampling is computationally infeasible. Such cases motivated the development of the Pearl's stochastic simulation algorithm. We have found that this stochastic simulation algorithm, when applied to certain networks, leads to much slower than expected convergence to the true posterior probabilities. This behavior is a result of the tendency for local areas in the network to become fixed through many simulation cycles. The time required to obtain significant convergence can be made arbitrarily long by strengthening the probabilistic dependency between nodes. We propose the use of several forms of graph modification, such as graph pruning, arc reversal, and node reduction, in order to convert some networks into formats that are computationally more efficient for simulation.

Advanced Decision Systems Abstract We present a thorough integration of hierarchical Bayesian inference with comprehensive physical representation of objects and their relations in a system for reasoning with geometry in machine vision. Bayesian inference provides a framework (or accruing probabilities to rank order hypotheses. This is a preliminary version of visual interpretation in SUCCESSOR, an intelligent, model-based vision system integrating multiple sensors. Introduction Our design for machine vision uses an evidential accrual process, a. beginning from representation and database of a priori models o(physical objects and their photometric, geometric, and functional properties, together with their relationships and environment, b. predicting observables using models of sensors and perceptual measurement processes; c. making measurements of corresponding observables, measuring image evidence for features of objects and structures of features such as edges, vertices and regions; d. generating hypotheses of instances o(objects from those measurements and predictions; and In range imagery, measurements are 3d. There is still a difficult stage of segmenting and estimating 3d relations that disclose object structure. In 2d images, there is an additional inference from 2d projected image evidence to 3d interpretation of surfaces. System structure tends to break up into a natural hierarchy of representation and processing [Binford 80).